Control of spiral turbulence by periodic forcing in a reaction-diffusion system with gradients.

We report an experimental result on successfully controlling spiral turbulence in a reaction-diffusion system. The control is realized by periodic forcing in a three-dimensional Belousov-Zhabotinsky reaction-diffusion system, which has chemical concentration gradients in the third dimension. We observe that, in the oscillatory regime of the system, a suitable periodic forcing may stabilize scroll waves (SWs), which otherwise undergo a transition to spiral turbulence. Relating the spiral phase shift due to gradients and the forcing frequency, the mechanism of the control can be well understood by modulating the phase twist of SWs. We use the FitzHugh-Nagumo model to demonstrate this mechanism.

Control of scroll wave turbulence in a three-dimensional reaction-diffusion system with gradient.

In this paper, we summarize our recent experimental and theoretical works on observation and control of scroll wave (SW) turbulence. The experiments were conducted in a three-dimensional Belousov-Zhabotinsky reaction-diffusion system with chemical concentration gradients in one dimension. A spatially homogeneous external forcing was used in the experiments as a control; it was realized by illuminating white light on the light sensitive reaction medium. We observed that, in the oscillatory regime of the system, SW can appear automatically in the gradient system, which will be led to spatiotemporal chaos under certain conditions. A suitable periodic forcing may stabilize inherent turbulence of SW. The mechanism of the transition to SW turbulence is due to the phase twist of SW in the presence of chemical gradients, while modulating the phase twist with a proper periodic forcing can delay this transition. Using the FitzHugh-Nagumo model with an external periodic forcing, we confirmed the control mechanism with numerical simulation. Moreover, we also show in the simulation that adding temporal external noise to the system may have the same control effect. During this process, we observed a new state called "intermittent turbulence," which may undergo a transition into a new type of SW collapse when the noise intensity is further increased. The intermittent state and the collapse could be explained by a random process.

Inward propagating chemical waves in a single-phase reaction-diffusion system.

We report our experimental and theoretical studies of inwardly propagating chemical waves (antiwaves) in a single-phase reaction-diffusion (RD) system. The experiment was conducted in an open spatial reactor using chlorite-iodide-malonic acid reaction. When the system was set to near Hopf bifurcation point, antiwaves appeared spontaneously, as predicted using both the reaction-diffusion (RD) equation and the complex Ginzburg-Landau equation (CGLE). Antiwaves change to ordinary waves when the system was moved away from the Hopf onset, which still agreed with RD simulations but could not be predicted by CGLE. We thus witnessed a new type of antiwave-wave exchange. Our analysis showed that this exchange occurred when the CGLE broke down as the system was far from the Hopf onset.

Effect of noise on chemical waves in three-dimensional reaction-diffusion systems with gradient.

The effect of noise on chemical waves in a quasi-three-dimensional reaction-diffusion medium with a gradient in the third dimension is studied using the FitzHugh-Nagumo model [R. FitzHugh, Biophysics J. 1, 445 (1961)]. Numerical simulations reveal that noise of appropriate intensity can postpone the onset of turbulence and stabilize the three-dimensional (3D) waves which would otherwise undergo the gradient-induced collapse. It is also found that the 3D waves can be interrupted by incident irregularities when the noise is not too strong; it can be induced into complete turbulence when the noise is strong enough. A mathematical analysis is given based on the dependence of the oscillation frequency on the control parameter. It agrees qualitatively with our numerical findings.